On the Clebsch-Gordan coefficients for the two-parameter quantum algebra $SU(2)_{p,q}$

TL;DR

This paper demonstrates that the Clebsch-Gordan coefficients for the two-parameter quantum algebra SU(2)_{p,q} depend only on a single combined parameter, simplifying previous explicit calculations.

Contribution

It reveals that the Clebsch-Gordan coefficients depend on a single parameter Q = √(pq), contrary to earlier findings that suggested dependence on two parameters.

Findings

Clebsch-Gordan coefficients depend on a single parameter Q

Contradicts previous explicit calculations by Smirnov and Wehrhahn

Simplifies understanding of the algebra's representation theory

Abstract

We show that the Clebsch - Gordan coefficients for the $SU(2)_{p,q}$ - algebra depend on a single parameter Q = $\sqrt{pq}$ ,contrary to the explicit calculation of Smirnov and Wehrhahn [J.Phys.A 25 (1992),5563].